## Elements of Geometry |

### From inside the book

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**equivalent**whose surfaces are equal . Two figures may be**equivalent**, however dissimilar ; thus a circle may be**equivalent**to a square , a triangle to a rectangle , & c . The denomination of equal figures will be restricted to those ... Page 45

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**equivalent**. Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 96 . two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the bases , will be situated in a ... Page 46

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**equivalent**. 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is**equivalent**to a rectangle of the same base and altitude . THEOREM . 2 Fig . 98 . 168. Every triangle ABC ( fig . 98 ) is half of a parallelogram ABCD of the same ... Page 53

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**equivalent**to the square AH , double of the triangle HBC . It may be demonstrated , in the same man- ner , that the rectangle CDEG is**equivalent**to the square AI ; but the two rectangles BDEF , CDEG , taken together , make the square ... Page 54

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**equivalent**to the squares AH , AI ; therefore , AB : AC :: BD : DC , or , the squares of the two sides of a right angle are to each other as the segments of the hypothenuse adjacent to these sides . Fig . 110 . THEOREM . 191. In a ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence